Periodic Lattice Research Articles

Stacking of charge-density waves in 2H−NbSe2 bilayers

We employ electronic-structure calculations to investigate the charge-density waves and periodic lattice distortions in bilayer 2H−NbSe2. We demonstrate that the vertical stacking can give rise to a variety of patterns that may lower the symmetry of the charge-density waves exhibited separately by the two composing 1H−NbSe2 monolayers. The general tendency to a spontaneous symmetry breaking observed in the ground state and the first excited states is shown to originate from a non-negligible interlayer coupling. Simulated images for scanning tunneling microscopy as well as geometric structure factors show signatures of the different stacking orders. This may not only be useful to reinterpret past experiments on surfaces and thin films, but it may also be exploited to devise ad hoc experiments for the investigation of the stacking order in 2H−NbSe2. We anticipate that our analysis not only applies to the 2H−NbSe2, but is also relevant for thin films and bulk, whose smallest centrosymmetric component is indeed the bilayer. Finally, our results illustrate clearly that the vertical stacking is not only important for 1T structures, as exemplified by the metal-to-insulator transition observed in 1T−TaS2, but seems to be a general feature of metallic layered transition metal dichalcogenides as well. Published by the American Physical Society 2024

High topological charge lasing in quasicrystals.

Photonic modes exhibiting a polarization winding akin to a vortex possess an integer topological charge. Lasing with topological charge 1 or 2 can be realized in periodic lattices of up to six-fold rotational symmetry-higher order charges require symmetries not compatible with any two-dimensional Bravais lattice. Here, we experimentally demonstrate lasing with topological charges as high as -5, +7, -17 and +19 in quasicrystals. We discover rich ordered structures of increasing topological charges in the reciprocal space. Our quasicrystal design utilizes group theory in determining electromagnetic field nodes, where lossy plasmonic nanoparticles are positioned to maximize gain. Our results open a new path for fundamental studies of higher-order topological defects, coherent light beams of high topological charge, and realizations of omni-directional, flat-band-like lasing.

Multianalyte Detection with Metasurface-Based Midinfrared Microspectrometer.

Midinfrared (2.5-25 μm) spectroscopy is an ideal tool for identifying chemicals in a nondestructive manner. The traditional platform is a Fourier transform infrared (FTIR) spectrometer, but this is too bulky, expensive, and power-hungry for many applications. There is therefore a growing demand for small, lightweight, and cost-effective microspectrometers for use in the field. One emerging platform is the filter-array detector-array microspectrometer. It pairs a broadband detector array with a thin and rigid array of spectral filters to offer a robust, compact platform for real-time in situ sensing. However, most demonstrations have only focused on identifying a single chemical against a null sample, even though many applications would involve multianalyte detection. In this work, we show a rare attempt at simultaneously tracking multiple analytes with a metasurface filter-array microspectrometer. The metasurface consists of periodic lattices of subwavelength circular apertures in an aluminum layer to create an array of bandpass filters. The filter array is imaged with an off-the-shelf microbolometer via a reverse-lens imaging setup to simultaneously monitor the concentration of ethanol and methanol in gasoline. This represents an important application of fuel quality monitoring. Chemometric models (PLS and SVR) are trained and tested on gasoline blends with ethanol and methanol contents, both ranging from 0% to 20% v/v. A support vector machine regression (SVR) model with a cubic kernel was found to have the lowest combined prediction errors. The root-mean-square-error of prediction (RMSEP) for ethanol and methanol are 1.23% and 1.84% v/v; the corresponding pseudounivariate limit of detection is found to be 4.22% and 6.86% v/v, respectively. This work takes the emerging field of metasurface-based mid-infrared spectrometers from single- to multianalyte detection, thereby considerably expanding their range of potential applications.

Standing Solitons Tuned by Impurities in Damped Nonlinear Lattices under External Excitation.

Periodic chains of nonlinear oscillators are known to support solitonic solutions within a specific range of physical parameters when damping effect is considered. This Letter investigates the dynamics of stationary solitons in damped nonlinear lattices under external excitation, focusing on the influence of impurities related to the natural frequency of the oscillators. We demonstrate experimentally and numerically that incorporating impurities into externally driven periodic lattices can expand the solitonic stability diagram under high-damping areas and near the Hopf bifurcation of periodic structures. A mathematical description that closely aligns with experimental realities is presented through the disordered damped nonlinear Schrödinger equation. Specifically, we prove how impurities along the chain can spontaneously nucleate the lattice solitons. The obtained results open the way toward the functionalization of disorder to control nonlinear energy localization in damped nonperiodic structures.

Stable Au(111) Hexagonal Reconstruction Induced by Perchlorinated Nanographene Molecules.

Surface reconstructions play a crucial role in surface science because of their influence on the adsorption and arrangement of molecules or nanoparticles. On the Au(111) surface, the herringbone reconstruction presents favorable anchoring at the elbow sites, where the highest reactivity is found. In this work, we deposited large organic perchlorinated molecules on a Au(111) surface via high-vacuum electrospray deposition. With noncontact atomic force microscopy measurements at room temperature, we studied the molecular structures formed on the surface before and after annealing at different temperatures. We found that a supramolecular layer is formed and that a hexagonal reconstruction of the Au(111) surface is induced. After high-temperature annealing, the molecules are removed, but the hexagonal Au(111) surface reconstruction is preserved. With the hexagonal Au(111) surface reconstruction, a periodic lattice of anchoring sites is formed.

Strain regulation retards natural operation decay of perovskite solar cells.

Perovskite solar cells (pero-SCs) have undergone a rapid development in the last decade. However, there is still a lack of systematic studies to investigate whether the empirical rules of working lifetime assessment used in silicon solar cells can be applied to pero-SCs. It is commonly believed that pero-SCs show enhanced stability under day/night cycling due to the reported self-healing effect in the dark.1,2 While we discovered that the degradation of highly efficient FAPbI3 pero-SCs is in fact much faster under natural day/night cycling mode, questioning the widely accepted approach to estimate the operational lifetime of pero-SCs based on continuous mode testing. We reveal the key factor to be the lattice strain caused by thermal expansion/shrinking of the perovskite during the operation, an effect that gradually relaxes under the continuous-illumination mode but cycles synchronously under the cycling mode.3,4 The periodic lattice strain under the cycling mode results in deep trap accumulation and chemical degradation during operation, decreasing the ion migration potential and hence the device lifetime.5 We introduce phenylselenenyl chloride (Ph-Se-Cl) to regulate the perovskite lattice strain during day/night cycling, which achieved the certified efficiency of 26.3% and a 10-time improved T80 lifetime under the cycling mode after the modification.

Sub-THz and THz Cherenkov radiation source with two-dimensional periodic surface lattice and multistage depressed collector

We present the theory, concept and design of an efficient, megawatt coherent Cherenkov radiation source based on a two-dimensional periodic surface lattice (2D-PSL) cavity combined with a novel energy recovery system for the generation of highly efficient (> 50%) single-frequency radiation. We demonstrate the scalability of the transverse dimension of the 2D-PSL cavity of the Cherenkov source and thus the potential for efficient, continuous-wave, high-power (> 1 MW) operation; fundamental to the eventual realization of clean, fusion energy. These new sources, with the capacity to operate in the 0.1-10THz range, hold strong promise to address the long-standing “Terahertz gap”. By combining a Cherenkov oscillator driven by a non-gyrating beam with an innovative four-stage depressed collector energy recovery system, the overall device efficiency can be increased to be competitive with gyrotrons in the requirements for heating and current drive in fusion plasma. In these Cherenkov devices, the frequency independence of the magnetic guide field enables advantageous frequency scaling without deployment constraints, making them especially attractive for high-impact applications in fusion science, turbulence diagnostics, non-destructive testing and biochemical spectroscopy. The novel energy recovery techniques presented in this paper have broad applicability to many electron-beam driven devices, bringing revolutionary potential to future THz source technologies.

Numerical study of dispersion characteristics of cylindrical spiral lines and periodic gratings based on them

Numerical studies of the dispersion characteristics of cylindrical spiral lines have been carried out. One-dimensional and two-dimensional periodic lattices formed by such lines are also considered. The eigenvalue method was used in combination with periodic boundary conditions. The dispersion characteristics are calculated in the range of parameters for which the conditions of applicability of the known approximate numerical-analytical methods for analyzing spiral lines are not met. The dispersion characteristics of the first two eigen-waves in one-dimensional and two-dimensional periodic lattices of spirals are obtained for different values of phase shifts between lattice periods. It is shown that the main type of wave in them is a wave slowed down relative to the axes of the lines with the direction of rotation of the field vector determined by the direction of winding of the spiral.

Extraordinary viscous absortion by phononic supercrystals

An effective medium theory has been developed to study the viscous absorption of a doubly periodic phononic crystal, here denominated as supercrystal (SC). In practice, the SC is made of hard cylindrical scatterers embedded in a viscous fluid and consists of a combination of two phononic crystals with lattice periods, $a_1$ and $a_2$. The decay coefficient of sound due to viscosity is calculated analytically at low frequencies when both lattices homogenize. The viscous absorbance of finite SC slabs calculated with the analytical model is supported by exact calculations based on the finite element method (COMSOL simulations). In addition, results for the complex sound speed show a good agreement with the experimentally extracted sound speed.

Bjerrum defects in s-II gas hydrate

The energy and structure of Bjerrum defects in structure II gas hydrates were investigated by using first-principle calculations for finite-size clusters and periodic 3D lattice systems. The formation energies of these defects were calculated for the first time when the cages of the structure II structure were completely empty and the large cage was filled with a THF molecule. Analogous to findings in ice structures, one of the hydrogen atoms forming the D defect was noted to orient toward the cage. If the excess proton resides in the large cage, it acts as an attraction center for the polar guest molecule, i.e., THF. Therefore, the large cage guest THF molecule stabilizes the D/L defect pair and isolated D/L defect formation energies by forming hydrogen bonds with the D defect. In such cases, the defect structure representing a D/L defect pair containing a THF molecule interacting with one of the hydrogen atoms of the D defect mirrors the guest-induced ones. Notably, the classical Bjerrum defect and the guest-induced Bjerrum defect exhibit a similar phenomenon in defective structures. Contrary to existing literature, it is evident that guest-induced Bjerrum defects involve both the L and D components. The insights gained from this study could potentially offer an alternative perspective to understand various experimental observations, such as those related to dielectric and NMR properties.

Topologically protected bound modes in non-neighboring hexagonal lattices

In the last decade, the study of wave localization and guiding has gained a renewed interest thanks to the introduction of the concept of topological protection. Originally developed in the field of quantum mechanics, topological protection has successively inspired the search for its analogue in other physical domains, including elasticity. In this context, periodic hexagonal lattices have been proposed as ideal candidates to realize these concepts. In this work, we explore the dynamic behavior of discrete hexagonal lattices with third nearest neighbor connections. First, the formation and transition of multiple Dirac cones above a critical value of the relative stiffness between the first and third nearest neighbor connections is derived. Then, the formation of extremely localized modes (i.e., bound modes) at the interface between regions formed by lattices which are inverted copies of each other is demonstrated. Our results show that this localization derives from a type of interface satisfying a point reflection symmetry for which the considered chain decouples into two identical copies at the high symmetry point of the Brillouin zone. Our findings open novel avenues for topological waveguiding and confinement with potential applications in surface acoustic wave devices.

Multi-objective topology optimization and numerical investigation of heat sinks based on triply periodic minimal surface lattices

In thermal management applications, such as heat sinks (HSs) for electronic devices, cellular materials have extensively been employed. In recent years, there has been a growing attention towards employing topology optimization for enhancing hydraulic and heat transfer performance of HSs by optimizing their topology. The utilization of triply periodic minimal surface (TPMS) based structures presents distinctive prospects for customizing the design and performance of HSs. However, their potential remains unexplored in the context of customizing additively manufactured porous optimized HSs. Consequently, there is a need for research aimed at examining their coupled hydraulic and thermal performance. Density mapping approaches are used to build a variable density TPMS-based HSs from the output of topology optimization by applying the TPMS level-set equations that relate relative density and the level-set constant. In this work, a relative density mapping methodology is applied to thermo-fluid optimization problem to design a TPMS-based convective cooling system. An in-house MATLAB code was developed to perform a multi-objective topology optimization. After that, uniform and variable density (mapped from topology optimization results) TPMS-based HSs are analyzed using Star-CCM + CFD software to investigate their hydraulic and heat transfer performance. An experimental setup was established, and the numerical results were validated using uniform TPMS-based heat sinks. Results showed that incorporating TPMS with topology optimization has a great potential in thermal management applications as pressure drop across the heat sink was reduced while maintaining the performance.

A review of structural diversity design and optimization for lattice metamaterials

Metamaterials are a type of groundbreaking engineered materials with unique properties not found in natural substances. Lattice metamaterials, which have a periodic lattice cell structure, possess exceptional attributes such as a negative Poisson’s ratio, high stiffness-to-weight ratios, and outstanding energy dissipation capabilities. This review provides a comprehensive examination of lattice metamaterials. It covers their various structures and fabrication methods. The review emphasizes the crucial role of homogenization methods and multi-scale modeling in assessing metamaterial properties. It also highlights the advancement of topology optimization through advanced computational techniques, such as finite element analysis simulations and machine learning algorithms.

Crashworthiness Investigations for 3D-Printed Multi-Layer Multi-Topology Engineering Resin Lattice Materials.

In comparison to monolithic materials, cellular solids have superior energy absorption capabilities. Of particular interest within this category are the periodic lattice materials, which offer repeatable and highly customizable behavior, particularly in combination with advances in additive manufacturing technologies. In this paper, the crashworthiness of engineering multi-layer, multi-topology (MLMT) resin lattices is experimentally examined. First, the response of a single- and three-layer single topology cubic and octet lattices, at a relative density of 30%, is investigated. Then, the response of MLMT lattices is characterized and compared to those single-topology lattices. Crashworthiness data were collected for all topology arrangements, finding that while the three-layer cubic and octet lattices were capable of absorbing 9.8 J and 7.8 J, respectively, up to their respective densification points, the unique MLMT lattices were capable of absorbing more: 19.0 J (octet-cube-octet) and 22.4 J (cube-octet-cube). These values are between 94% and 187% greater than the single-topology clusters of the same mass.

Electrified reformer for syngas production – Additive manufacturing of coated microchannel monolithic reactor

Here, an electrified reformer with a bespoke design of catalyst-coated and additively manufactured monoliths with 3-D pore architecture is presented. The 2D-pore architecture of the hexagonal honeycomb monolith was compared against the 3D-pore architecture of three broad classifications - triply periodic minimal surface (Gyroid), strut-based (Octet) and stochastic lattice (Voronoi). Gyroid structured reactor, coated with NiO/Ce0.8Gd0.2O2-δ catalyst and heated to 900 °C achieved >99 % conversion of CO2 and CH4 at WHSV = 11,000 L.h−1.kgcat−1, while remaining active for >42 h with no evidence of coke deposition. Whereas Octet and Voronoi reactors showed slightly lower conversions, with 6-fold and 4-fold higher pressure drops, respectively. This study combines Computational Fluid Dynamics and experimental evidence to reveal that the Gyroid lattice provides high catalyst deposition and catalytic activity at low pressure drops. This study demonstrates the feasibility of renewable energy-powered structured reactors to provide a pathway for low carbon footprint chemical production.

The deformation mechanism of low symmetric Ti–Pt intermetallic compounds containing high density of planar defects

Intermetallic compounds typically exhibit limited plastic deformation capacity due to challenges in activating dislocation slip and deformation twinning, coupled with a lack of alternative deformation mechanisms. Ti–Pt alloys are a prevalent type of intermetallic compound utilized in high-temperature shape memory alloys and as materials for energy applications in electric fields. However, they often exhibit poor deformation capability. Here, we prepared a low-symmetry intermetallic phase, Ti4Pt3, which demonstrates significant plastic deformation capability. This phase features a high density of parallel planar defects, resulting in an exceptionally large lattice periodicity perpendicular to these defects. Through in-situ scanning electron microscope compression tests, we observed substantial plastic deformation in this new phase. Analysis of the deformed Ti4Pt3 phase revealed that the dense planar defects create uniformly distributed sites of internal stress concentration, enabling a rapid increase in back stress within crystals. This phenomenon leads to notable lattice rotation and localized order-disorder transitions, both crucial mechanisms facilitating plastic deformation and enhancing deformation capacity. Our research underscores the potential of leveraging structural asymmetry to enable unconventional deformation mechanisms, thereby enhancing the plasticity of intermetallic materials.

Observation of nonlinear fractal higher order topological insulator

Higher-order topological insulators (HOTIs) are unique materials hosting topologically protected states, whose dimensionality is at least by 2 lower than that of the bulk. Topological states in such insulators may be strongly confined in their corners which leads to considerable enhancement of nonlinear processes involving such states. However, all nonlinear HOTIs demonstrated so far were built on periodic bulk lattice materials. Here, we demonstrate the first nonlinear photonic HOTI with the fractal origin. Despite their fractional effective dimensionality, the HOTIs constructed here on two different types of the Sierpiński gasket waveguide arrays, may support topological corner states for unexpectedly wide range of coupling strengths, even in parameter regions where conventional HOTIs become trivial. We demonstrate thresholdless spatial solitons bifurcating from corner states in nonlinear fractal HOTIs and show that their localization can be efficiently controlled by the input beam power. We observe sharp differences in nonlinear light localization on outer and multiple inner corners and edges representative for these fractal materials. Our findings not only represent a new paradigm for nonlinear topological insulators, but also open new avenues for potential applications of fractal materials to control the light flow.

Tailoring elastic bandgaps and moduli of triply periodic minimal surface structures by a hybrid technique

This work aimed to investigate elastic dispersion behaviors of triply periodic minimal surface (TPMS) lattice structures. The dispersion curves were established using the finite element (FE) Bloch reduction method, in which the Bloch periodic boundary condition was implied via the Bloch transform matrix. Four different types of both surface- and solid-based TPMS lattices with varying relative densities were considered. It was found that only the solid-based Neovius and Schwarz structures provided complete elastic bandgaps. Then, elastic stiffnesses of the structures obtained by representative volume element (RVE) models were evaluated with regard to their achieved band gaps. Reducing the volume fraction of lattices obviously enhanced the bandgap behaviors, while decreasing the specific moduli. Moreover, new hybrid phononic lattices were introduced for tailoring the elastic bandgap and mechanical properties. The results showed that incorporating the strut-based face-centered cubic (FCC) lattice in the TPMS structures could obviously improve the bandgap characteristics and simultaneously maintain reasonable specific elastic properties. Finally, wave suppression structure by using the dispersion curves was demonstrated by examining a simple beam infilled with the periodic lattices under excited loads. It was shown that the TPMS structures could be well applied as an effective wave suppression feature in load-bearing structures.

Janus Monolayer of 1T-TaSSe: A Computational Study.

Materials exhibiting charge density waves are attracting increasing attention owing to their complex physics and potential for applications. In this paper, we present a computational, first principles-based study of the Janus monolayer of 1T-TaSSe transition metal dichalcogenide. We extensively compare the results with those obtained for parent compounds, TaS2 and TaSe2 monolayers, with confirmed presence of 13×13 charge density waves. The structural and electronic properties of the normal (undistorted) phase and distorted phase with 13×13 periodic lattice distortion are discussed. In particular, for a normal phase, the emergence of dipolar moment due to symmetry breaking is demonstrated, and its sensitivity to an external electric field perpendicular to the monolayer is investigated. Moreover, the appearance of imaginary energy phonon modes suggesting structural instability is shown. For the distorted phase, we predict the presence of a flat, weakly dispersive band related to the appearance of charge density waves, similar to the one observed in parent compounds. The results suggest a novel platform for studying charge density waves in two-dimensional transition metal dichalcogenides.

Mott Transition for a Lieb-Liniger Gas in a Shallow Quasiperiodic Potential: Delocalization Induced by Disorder.

Disorder or quasidisorder is known to favor localization in many-body Bose systems. Here, in contrast, we demonstrate an anomalous delocalization effect induced by incommensurability in quasiperiodic lattices. Loading ultracold atoms in two shallow periodic lattices with equal amplitude and either equal or incommensurate spatial periods, we show the onset of a Mott transition not only in the periodic case but also in the quasiperiodic case. Switching from periodic to quasiperiodic potential with the same amplitude, we find that the Mott insulator turns into a delocalized superfluid. Our experimental results agree with quantum MonteCarlo calculations, showing this anomalous delocalization induced by the interplay between the disorder and interaction.